Compressible stability of growing boundary layers is studied by numerically solving the partial differential equations under a parabolizing approximation. The resulting parabolized stability equations (PSE) account for nonparallel as well as nonlinear effects. Evolution of disturbances in compressible flat-plate boundary layers are studied for freestream Mach numbers ranging from 0 to 4.5. Results indicate that the effect of boundary-layer growth is important for linear disturbances. Nonlinear calculations are performed for various Mach numbers. Two-dimensional nonlinear results using the PSE approach agree well with those from direct numerical simulations using the full Navier- Stokes equations while the required computational time is less by an order of magnitude. Spatial simulations using PSE have been carried out for both the fundamental and subharmonic type breakdown for a Mach 1.6 boundary layer. The promising results obtained in this study show that the PSE method is a powerful tool for studying boundary-layer instabilities and for predicting transition over a wide range of Mach numbers. Stability, Compressible, Boundary layer, PSE.

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